Characterization of bioheat transport using an exact solution of the cylindrical geometry, multi-region, time-dependent bioheat equation

Bioheat transfer problem for one-dimensional spherical biological tissues

Based on the Pennes bioheat transfer equation with constant blood perfusion, we set up a simplified one-dimensional bioheat transfer model of the spherical living biological tissues for application in bioheat transfer problems. Using the method of separation of variables, we present in a simple way the analytical solution of the problem. The obtained exact solution is used to investigate the effects of tissue properties, the cooling medium temperature, and the point-heating on the temperature distribution in living bodies. The obtained analytical solution can be useful for investigating thermal behavior research of biological system, thermal parameter measurements, temperature field reconstruction and clinical treatment.

Study of the one dimensional and transient bioheat transfer equation: multi-layer solution development and applications

In this work we derive an analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp). The convective heat transfer effect of a large blood vessel located inside the brain is also investigated. The results are further compared with a numerical solution obtained by the Finite Element Method and computed with COMSOL Multiphysics v4.1©.

Solution to the bioheat equation for hyperthermia with La(1-x)Ag(y)MnO(3-delta) nanoparticles: the effect of temperature autostabilization

This work aimed to analyze the possibility and performance of the temperature controlled hyperthermia based on AC heating of magnetic nanoparticles with low Curie temperature. Temperature dependence of dynamic magnetic susceptibility has been studied experimentally on fine powders of La(0.8)Ag(0.15)MnO(2.95) in the frequency range of 0.5-2.0 MHz. Critical drop of the AC magnetic losses was found in the vicinity of the Curie point, T(C) = 42 degrees C. The obtained data was used in the numerical analysis of the bioheat equations under typical conditions of the hyperthermia treatment. The mathematical model includes a spherical tumor containing magnetic particles and surrounded by concentric healthy tissue, with account made for the blood perfusion. The calculations performed for various AC power, tumor sizes and doping geometries predict effective autostabilization of the temperature at T congruent with T(C) inside the tumor and steep temperature profile at the interface with the healthy tissue.

Transient solution to the bioheat equation and optimization for magnetic fluid hyperthermia treatment

Two finite concentric spherical regions were considered as the tissue model for magnetic fluid hyperthermia treatment. The inner sphere represents the diseased tissue containing magnetic particles that generate heat when an alternating magnetic field is applied. The outer sphere represents the healthy tissue. Blood perfusion effects are included in both the regions. Analytical and numerical solutions of the one-dimensional bioheat transfer equation were obtained with constant and spatially varying heat generation in the inner sphere. The numerical solution was found to be in good agreement with the analytical solution. In an ideal hyperthermia treatment, all the diseased tissues should be selectively heated without affecting any healthy tissue. The present work optimized the magnetic particle concentration in an attempt to achieve the ideal hyperthermia conditions. It was found that, for a fixed amount of magnetic particles, optimizing the magnetic particle distribution in the diseased tissue can significantly enhance the therapeutic temperature levels in the diseased tissue while maintaining the same level of heating in the healthy tissue.

Analytical study on bioheat transfer problems with spatial or transient heating on skin surface or inside biological bodies

Several closed form analytical solutions to the bioheat transfer problems with space or transient heating on skin surface or inside biological bodies were obtained using Green's function method. The solutions were applied to study several selected typical bioheat transfer processes, which are often encountered in cancer hyperthermia, laser surgery, thermal comfort analysis, and tissue thermal parameter estimation. Thus a straightforward way to quantitatively interpret the temperature behavior of living tissues subject to constant, sinusoidal, step, point or stochastic heatings etc. both in volume and on boundary were established. Further solution to the three-dimensional bioheat transfer problems was also given to illustrate the versatility of the present method. Implementations of this study to the practical problems were addressed.